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Activity Number: 625
Type: Invited
Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
Sponsor: International Chinese Statistical Association
Abstract #314554 View Presentation
Title: Minimax Matrix Regression Function Estimation for Symmetric Positive Definite Matrices
Author(s): Peter T. Kim*
Companies: University of Guelph
Keywords: Cholesky decomposition ; diffusion tensor imaging ; spline estimation
Abstract:

Symmetric positive-definite (SPD) matrix data commonly appear in computer vision and medical imaging, such as diffusion tensor imaging (DTI). We develop a nonparametric estimation of a SPD matrix response given covariates. We first derive a lower bound on the rate of convergence under the assumption that the Kullback-Leibler divergence between the conditional distributions for the response given covariates has a quadratic bound. This lower bound technique based on the Cholesky decomposition is of independent interest and can be used for other conditional matrix estimation problems. We then establish that this lower bound is actually a minimax optimal rate of convergence. In order to address the finite-sample performance of the proposed methodology, we have carried out a numerical study using both simulated and real data. A simulation study shows that that the proposed method using natural splines estimates the underlying covariance matrix reasonably well. Moreover, we present the results on an analysis of real DTI data where the estimated fractional anisotropy is provided using 3 × 3 SPD matrices measured at consecutive positions along a fiber tract in the brain of subjects.


Authors who are presenting talks have a * after their name.

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